A reconstruction method is generally known as WFBP reconstruction. Reference is made by way of example in this regard to the publication by Stierstorfer et al., Phys. Med. Biol. 49 pp. 2209-2218, 2004, in which such a reconstruction by weighted filtered backprojection is disclosed.
Such a WFBP method is usually made up of four steps, with a conversion from cone beam detector data to parallel data generally being used for practical reasons, to facilitate the actual reconstruction from a computation point of view.
In the first step raw detector data is measured with a CT system, with the discrete coordinates used here being related as follows to the continuous coordinates:β=β0+kβΔβ,q=q0+kqΔq, α=α0+kαΔα,where β describes the fan angle of the measurement beam, q the detector channel and α the angular position of the focus, and β0, q0, α0 respectively describe the start of measurement and Δβ, Δq, Δα respectively describe the increments of the measurement steps.
In the second step of the WFBP method the existing cone beam detector data Praw[kβ, kq, kα] rebinned to rebinned parallel projection data Praw[kp, kq, kθ]. A transition is made here from discrete cone beam coordinates β, q, α to discrete parallel beam coordinates p, q, θ, with p representing the channel index, q the detector row coordinate and θ the parallel projection angle.
In the third step the rebinned parallel projection data Preb[kp, kq, kθ] is convolved with a ramp filter to produce the convolved projection data Pconv(p, q, θ), the geometry of the data not changing here.
In the fourth and last step the convolved projection data is backprojected onto the volume to be reconstructed. This is described mathematically by the formula
      V          x      ,      y      ,      z        =            ∑      θ                            ⁢                  ⁢                  1                              ∑            k                                                          ⁢                                          ⁢                      W            ⁡                          (              q              )                                          ⁢                        ∑          k                                                ⁢                                  ⁢                              W            ⁡                          (              q              )                                ·                                    P              conv                        ⁡                          (                              p                ,                q                ,                                  θ                  +                                      k                    ⁢                                                                                  ⁢                    π                                                              )                                          where Vx,y,z corresponds to the value of the reconstructed image voxel at the Cartesian coordinates x, y and z of a CT representation, Pconv(p, q, θ+kπ) represents the convolved and rebinned projection data in parallel coordinates, where k is a whole number, which represents the number of half rotations of the detector during scanning, the detector row coordinate q describes a central beam of the image voxel Vx,y,Z projected onto the detector at point x, y, z in the system axis direction with values between −1 and +1 standardized over the detector width and W(q) represents a detector row coordinate-dependent weighting function, which weights rows at the edges of the detector in a decreasing manner toward the edge for artifact reduction.
In principle such a method gives rise to the problem that a projection of an image voxel onto a scanning detector only seldom strikes the center of a detector row. It is therefore necessary to calculate the projection data used to perform the WFBP reconstruction initially from adjacent detector data, in some instances after prior rebinning to parallel data, by way of interpolation. In one particularly simple variant only detector data from directly adjacent detector rows is used.
This has the disadvantage that the spatial resolution of the resulting images in the z direction deteriorates due to the interpolation of the projection data from detector data.